Properties

Base field \(\Q(\sqrt{-11}) \)
Weight 2
Level norm 240
Level \( \left(8 a - 12\right) \)
Label 2.0.11.1-240.1-a
Dimension 1
CM no
Base-change no
Sign -1
Analytic rank odd

Related objects

Learn more about

Base Field: \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 3\); class number \(1\).

Form

Weight 2
Level 240.1 = \( \left(8 a - 12\right) \)
Label 2.0.11.1-240.1-a
Dimension: 1
CM: no
Base change: no
Newspace:2.0.11.1-240.1 (dimension 1)
Sign of functional equation: -1
Analytic rank: odd

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -a \)) \( -1 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( 0 \)
\( 4 \) 4.1 = (\( 2 \)) \( 0 \)
\( 5 \) 5.1 = (\( -a - 1 \)) \( -1 \)
\( 5 \) 5.2 = (\( a - 2 \)) \( 0 \)
\( 11 \) 11.1 = (\( -2 a + 1 \)) \( -2 \)
\( 23 \) 23.1 = (\( a + 4 \)) \( -6 \)
\( 23 \) 23.2 = (\( a - 5 \)) \( -4 \)
\( 31 \) 31.1 = (\( -3 a + 4 \)) \( 10 \)
\( 31 \) 31.2 = (\( 3 a + 1 \)) \( 0 \)
\( 37 \) 37.1 = (\( -3 a - 2 \)) \( -6 \)
\( 37 \) 37.2 = (\( 3 a - 5 \)) \( -4 \)
\( 47 \) 47.1 = (\( -2 a + 7 \)) \( -8 \)
\( 47 \) 47.2 = (\( 2 a + 5 \)) \( -8 \)
\( 49 \) 49.1 = (\( 7 \)) \( 8 \)
\( 53 \) 53.1 = (\( -4 a + 5 \)) \( -2 \)
\( 53 \) 53.2 = (\( 4 a + 1 \)) \( -2 \)
\( 59 \) 59.1 = (\( a + 7 \)) \( 0 \)
\( 59 \) 59.2 = (\( a - 8 \)) \( -4 \)
\( 67 \) 67.1 = (\( -3 a - 5 \)) \( -10 \)
\( 67 \) 67.2 = (\( 3 a - 8 \)) \( 12 \)
\( 71 \) 71.1 = (\( -5 a + 1 \)) \( -8 \)
\( 71 \) 71.2 = (\( 5 a - 4 \)) \( -8 \)
\( 89 \) 89.1 = (\( 5 a + 2 \)) \( 14 \)
\( 89 \) 89.2 = (\( 5 a - 7 \)) \( 8 \)
\( 97 \) 97.1 = (\( -3 a + 10 \)) \( -12 \)
\( 97 \) 97.2 = (\( 3 a + 7 \)) \( -2 \)
\( 103 \) 103.1 = (\( -6 a + 1 \)) \( 6 \)
\( 103 \) 103.2 = (\( 6 a - 5 \)) \( -8 \)
\( 113 \) 113.1 = (\( a + 10 \)) \( 6 \)
\( 113 \) 113.2 = (\( a - 11 \)) \( 6 \)
\( 137 \) 137.1 = (\( 7 a - 5 \)) \( 4 \)
\( 137 \) 137.2 = (\( 7 a - 2 \)) \( -2 \)
\( 157 \) 157.1 = (\( -3 a + 13 \)) \( 14 \)
\( 157 \) 157.2 = (\( 3 a + 10 \)) \( 10 \)
\( 163 \) 163.1 = (\( -6 a - 5 \)) \( -4 \)
\( 163 \) 163.2 = (\( 6 a - 11 \)) \( 10 \)
\( 169 \) 169.1 = (\( 13 \)) \( 2 \)
\( 179 \) 179.1 = (\( -5 a + 13 \)) \( 4 \)
\( 179 \) 179.2 = (\( -5 a - 8 \)) \( 12 \)
\( 181 \) 181.1 = (\( -3 a - 11 \)) \( -2 \)
\( 181 \) 181.2 = (\( 3 a - 14 \)) \( -26 \)
\( 191 \) 191.1 = (\( -7 a + 11 \)) \( 24 \)
\( 191 \) 191.2 = (\( -7 a - 4 \)) \( -20 \)
\( 199 \) 199.1 = (\( -6 a + 13 \)) \( 4 \)
\( 199 \) 199.2 = (\( 6 a + 7 \)) \( -24 \)
\( 223 \) 223.1 = (\( -9 a + 5 \)) \( -16 \)
\( 223 \) 223.2 = (\( -9 a + 4 \)) \( -12 \)
\( 229 \) 229.1 = (\( 9 a - 7 \)) \( 22 \)
\( 229 \) 229.2 = (\( 9 a - 2 \)) \( -14 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 4 \) 4.1 = (\( 2 \)) \( 1 \)
\( 3 \) 3.1 = (\( -a \)) \( 1 \)
\( 5 \) 5.1 = (\( -a - 1 \)) \( 1 \)